ARROW-638: [C++] Complex Number Support

[sjperkins]

xref https://issues.apache.org/jira/browse/ARROW-638

Added COMPLEX_FLOAT and COMPLEX_DOUBLE types to the flatbuffers definition in feather.fbs as an initial stab.

This is a draft and I've some questions before proceeding foreward:

• Complex valued types are standard types so my impression would be that base types should exist for them in Arrow.
• But this looks like it may be a breaking format change (V5 to V6). Is this undesirable?
• Alternatively, what would be lost by implementing this as an C++ Extension Type?

[github-actions]

Thanks for opening a pull request!

If this is not a minor PR. Could you open an issue for this pull request on JIRA? https://issues.apache.org/jira/browse/ARROW

Opening JIRAs ahead of time contributes to the Openness of the Apache Arrow project.

Then could you also rename pull request title in the following format?

ARROW-${JIRA_ID}: [${COMPONENT}] ${SUMMARY}

or

MINOR: [${COMPONENT}] ${SUMMARY}

See also:

• Other pull requests
• Contribution Guidelines - How to contribute patches

[pitrou]

I think it would be best to start a discussion on the dev mailing-list to gauge interest and support for this. @sjperkins Do you want to do it?

[github-actions]

https://issues.apache.org/jira/browse/ARROW-638

[sjperkins]

#10565 contains the PR implementing Complex Numbers as Extension Types